# Anova? Chi-square?

#### jamesmartinn

##### Member
Hi,

I've been asked to analyze some data and I wanted to get a second opinion on the way I plan to.

I have a sample of 8000 teachers. For each teacher, I have their Teaching Specialty, Total Number of Nights they worked and Total number of day-time days they worked, following working the previous night.

The quantity of interest is: #total number of day-time days they worked following working the previous night / total number of nights they worked.

I want to report the overall proportion, each proportion for each teaching type and then compare the proportions across teaching type.

I'm a bit confused on how to proceed. My gut tells me to just manually create a new variable by dividing the totals appropriately, then run an ANOVA. Would a Chi Square work here? That's what they had in mind.

Cheers,

#### hlsmith

##### Less is more. Stay pure. Stay poor.
A little confused by your description of the variables, but you can definitely test the equality of multiple proportions with chi square using an omnibus test (all groups in it at once). Then if significant, conduct pairwise comparisons, correcting for your familywise error rate.

Are you thinking ANOVA because you will have average proportions per teaching specialty?

#### jamesmartinn

##### Member
Thanks hlsmith. I'll go over them again, with an example (they are kind of confusing)

Code:
Teacher ID    Sub-Specialty  #A   #B   #C
12345           Biology            5      2     0.40
67891           Math               4      2     0.50
23234           Chem              4      0     0.00
99999           Biology           10     2     0.20
This is how my data is set up - at the individual teacher level. For each teacher, I got their sub-specialty. #A refers to how many days they worked over night. #B is how many days they worked the next day after working a night. #C is just #A/#B.

For example the Bio teacher, s/he worked a total of 5 nights at the school (Say mon-fri). After their shift was up, they went to their secondary job immediately twice (Say on thurs-fri) that week.

How could I use a Chi Square test here? My understanding is that they want quantity #C, which is #B#A. Can a Chi Square test directly for quantity #C?

#### Karabiner

##### TS Contributor
If the DV is a proportion (not a categorical measure) I suppose
that a Kruskal-Wallis H-test could be used (or a oneway ANOVA, but
I am not sure about the behaviour of proportions as DVs).

With kind regards

K.

#### GretaGarbo

##### Human
I would suggest a logit regression = logistic regression, where #C is the response variable and #B is the “n”, the number of trials. For the biology teacher the response was 2 and the number of trials was 5. The sub-speciality would be a fixed effects and the teacher ID a random effect.